The identification of complex semantic structures such as events and entity relations, already a challenging Information Extraction task, is doubly difficult from sources written in under-resourced and under-annotated languages. We investigate the suitability of crosslingual structure transfer techniques for these tasks. We exploit relation- and event-relevant language-universal features, leveraging both symbolic (including part-of-speech and dependency path) and distributional (including type representation and contextualized representation) information. By representing all entity mentions, event triggers, and contexts into this complex and structured multilingual common space, using graph convolutional networks, we can train a relation or event extractor from source language annotations and apply it to the target language. Extensive experiments on cross-lingual relation and event transfer among English, Chinese, and Arabic demonstrate that our approach achieves performance comparable to state-of-the-art supervised models trained on up to 3,000 manually annotated mentions: up to 62.6% F-score for Relation Extraction, and 63.1% F-score for Event Argument Role Labeling. The event argument role labeling model transferred from English to Chinese achieves similar performance as the model trained from Chinese. We thus find that language-universal symbolic and distributional representations are complementary for cross-lingual structure transfer.